Example 20.12. Censoring in the Tobit and Poisson Regression Models

/*======

*/======

? (continued)

Dstat ; Rhs=*

Histogram;rhs=y$

Descriptive Statistics

All results based on nonmissing observations.

======

Variable Mean Std.Dev. Minimum Maximum Cases

======

Y 1.45590682 3.29875773 .000000000 12.0000000 601

Z1 .475873544 .499833583 .000000000 1.00000000 601

Z2 32.4875208 9.28876170 17.5000000 57.0000000 601

Z3 8.17769551 5.57130315 .125000000 15.0000000 601

Z4 .715474210 .451564115 .000000000 1.00000000 601

Z5 3.11647255 1.16750940 1.00000000 5.00000000 601

Z6 16.1663894 2.40255457 9.00000000 20.0000000 601

Z7 4.19467554 1.81944266 1.00000000 7.00000000 601

Z8 3.93178037 1.10317949 1.00000000 5.00000000 601

Histogram for Y NOBS= 601, Too low: 0, Too high: 0

Bin Lower limit Upper limit Frequency Cumulative Frequency

======

0 .000 1.000 451 ( .7504) 451( .7504)

1 1.000 2.000 34 ( .0566) 485( .8070)

2 2.000 3.000 17 ( .0283) 502( .8353)

3 3.000 4.000 19 ( .0316) 521( .8669)

4 4.000 5.000 0 ( .0000) 521( .8669)

5 5.000 6.000 0 ( .0000) 521( .8669)

6 6.000 7.000 0 ( .0000) 521( .8669)

7 7.000 8.000 42 ( .0699) 563( .9368)

8 8.000 9.000 0 ( .0000) 563( .9368)

9 9.000 10.000 0 ( .0000) 563( .9368)

10 10.000 11.000 0 ( .0000) 563( .9368)

11 11.000 12.000 0 ( .0000) 563( .9368)

12 12.000 13.000 38 ( .0632) 601(1.0000)

? Specification analysis for the tobit model

Create ;q=y>0$

Namelist ; X = one,z1,z2,z3,z4,z5,z6,z7,z8 $

Namelist ; Xr= one, z2,z3, z5, z7,z8 $

? Tobit specification tests for three variables

? Wald

Tobit ; Lhs = y ; Rhs = X ; Wald:b(2)=0,b(5)=0,b(7)=0$

Calc ; LogLU=Logl $

Tobit ; Lhs = y ; Rhs = XR$

? Likelihood Ratio

Calc ; List ; LogLR=Logl ; LRTest = -2*(LogLR - LogLu) $

? lagrange Multiplier

Tobit ; Lhs = y ; Rhs = X ; Maxit = 0

; Start=b(1),0,b(2),b(3),0,b(4),0,b(5),b(6),s$

+------+

| Limited Dependent Variable Model - CENSORED |

| Log likelihood function -704.7311 |

| Threshold values for the model: |

| Lower= .0000 Upper=+infinity |

| Wald test of 3 linear restrictions |

| Chi-squared = 1.66, Sig. level = .64546 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Primary Index Equation for Model

Constant 7.608487071 3.9059870 1.948 .0514

Z1 .9457873252 1.0628656 .890 .3735 .47587354

Z2 -.1926982765 .80968360E-01 -2.380 .0173 32.487521

Z3 .5331896065 .14660745 3.637 .0003 8.1776955

Z4 1.019181783 1.2795746 .797 .4257 .71547421

Z5 -1.698999723 .40548331 -4.190 .0000 3.1164725

Z6 .2536077921E-01 .22766679 .111 .9113 16.166389

Z7 .2129825522 .32115700 .663 .5072 4.1946755

Z8 -2.273284428 .41540687 -5.472 .0000 3.9317804

Disturbance standard deviation

Sigma 8.258432069 .55458061 14.891 .0000

+------+

| Limited Dependent Variable Model - CENSORED |

| Log likelihood function -705.5762 |

| Threshold values for the model: |

| Lower= .0000 Upper=+infinity |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Primary Index Equation for Model

Constant 8.174197436 2.7414456 2.982 .0029

Z2 -.1793325837 .79093240E-01 -2.267 .0234 32.487521

Z3 .5541418128 .13451794 4.119 .0000 8.1776955

Z5 -1.686220493 .40375155 -4.176 .0000 3.1164725

Z7 .3260532488 .25442475 1.282 .2000 4.1946755

Z8 -2.284972720 .40782792 -5.603 .0000 3.9317804

Disturbance standard deviation

Sigma 8.247080326 .55336401 14.904 .0000

LRTEST = .16903037971408140D+01

Maximum iterations reached. Exit iterations with status=1.

Maxit = 0. Computing LM statistic at starting values.

No iterations computed and no parameter update done.

+------+

| Limited Dependent Variable Model - CENSORED |

| Iterations completed 1 |

| LM Stat. at start values 1.681409 |

| LM statistic kept as scalar LMSTAT |

| Log likelihood function -705.5762 |

| Threshold values for the model: |

| Lower= .0000 Upper=+infinity |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Primary Index Equation for Model

Constant 8.174197436 3.8998101 2.096 .0361

Z1 .0000000000 1.0537723 .000 1.0000 .47587354

Z2 -.1793325837 .80623305E-01 -2.224 .0261 32.487521

Z3 .5541418128 .14686554 3.773 .0002 8.1776955

Z4 .0000000000 1.2675769 .000 1.0000 .71547421

Z5 -1.686220493 .40440804 -4.170 .0000 3.1164725

Z6 .0000000000 .22719456 .000 1.0000 16.166389

Z7 .3260532488 .31951084 1.020 .3075 4.1946755

Z8 -2.284972720 .41462602 -5.511 .0000 3.9317804

Disturbance standard deviation

Sigma 8.247080326 .55345418 14.901 .0000

? Get main results, and MLEs. OLS is part of output

Tobit ; Lhs = y ; Rhs = XR ; MarginalEffects ; Par ; OLS $

Calc ; List ; Ltobit=Logl $

? Scaled tobit estimates and standard errors

Wald ; Start=B ; Var=varb ; labels=b1,b2,b3,b4,b5,b6,sg

; fn1=b1/sg ; fn2=b2/sg ; fn3=b3/sg

; fn4=b4/sg ; fn5=b5/sg ; fn6=b6/sg$

? Cragg/Greene consistency test for probability

Create ; q = y>0 $

Probit ; Lhs=q ; Rhs=xr ; Marginals$

Calc ; Lprobit=Logl $

Trunc ; Lhs=y ; Rhs=Xr ; Marginals $

Calc ; LTrunc=Logl $

Calc ; List ; Cragg = -2*(Ltobit - Lprobit - Ltrunc) $

+------+

| Limited Dependent Variable Model - CENSORED Regression |

| Ordinary least squares regression Weighting variable = none |

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 5.608160612 .79659947 7.040 .0000

Z2 -.5034734786E-01 .22105810E-01 -2.278 .0228 32.487521

Z3 .1618520786 .36896903E-01 4.387 .0000 8.1776955

Z5 -.4763238840 .11130785 -4.279 .0000 3.1164725

Z7 .1060059379 .71100666E-01 1.491 .1360 4.1946755

Z8 -.7122423539 .11828889 -6.021 .0000 3.9317804

+------+

| Limited Dependent Variable Model - CENSORED |

| Log likelihood function -705.5762 |

| Threshold values for the model: |

| Lower= .0000 Upper=+infinity |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Primary Index Equation for Model

Constant 8.174197436 2.7414456 2.982 .0029

Z2 -.1793325837 .79093240E-01 -2.267 .0234 32.487521

Z3 .5541418128 .13451794 4.119 .0000 8.1776955

Z5 -1.686220493 .40375155 -4.176 .0000 3.1164725

Z7 .3260532488 .25442475 1.282 .2000 4.1946755

Z8 -2.284972720 .40782792 -5.603 .0000 3.9317804

Disturbance standard deviation

Sigma 8.247080326 .55336401 14.904 .0000

+------+

| Partial derivatives of expected val. with |

| respect to the vector of characteristics. |

| They are computed at the means of the Xs. |

| Conditional Mean at Sample Point 1.1263 |

| Scale Factor for Marginal Effects .2338 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 1.910805170 .65758415 2.906 .0037

Z2 -.4192088958E-01 .18444435E-01 -2.273 .0230 32.487521

Z3 .1295365141 .31167559E-01 4.156 .0000 8.1776955

Z5 -.3941718881 .93379144E-01 -4.221 .0000 3.1164725

Z7 .7621839800E-01 .59471640E-01 1.282 .2000 4.1946755

Z8 -.5341365586 .94896126E-01 -5.629 .0000 3.9317804

LTOBIT = -.70557621764203170D+03

+------+

| WALD procedure. Estimates and standard errors |

| for nonlinear functions |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Fncn( 1) .9911625827 .33652215 2.945 .0032

Fncn( 2) -.2174497842E-01 .95484533E-02 -2.277 .0228

Fncn( 3) .6719248399E-01 .16136495E-01 4.164 .0000

Fncn( 4) -.2044627222 .48371582E-01 -4.227 .0000

Fncn( 5) .3953559755E-01 .30825623E-01 1.283 .1996

Fncn( 6) -.2770644434 .48258618E-01 -5.741 .0000

+------+

| Binomial Probit Model |

| Log likelihood function -307.2955 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant .9766647244 .36104809 2.705 .0068

Z2 -.2202376072E-01 .10177371E-01 -2.164 .0305 32.487521

Z3 .5990084920E-01 .17086004E-01 3.506 .0005 8.1776955

Z5 -.1836462412 .51493239E-01 -3.566 .0004 3.1164725

Z7 .3751312008E-01 .32844576E-01 1.142 .2534 4.1946755

Z8 -.2729824396 .52473295E-01 -5.202 .0000 3.9317804

+------+

| Partial derivatives of E[y] = F[*] with |

| respect to the vector of characteristics. |

| They are computed at the means of the Xs. |

| Observations used for means are All Obs. |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant .2969094977 .11108860 2.673 .0075

Z2 -.6695300413E-02 .30909282E-02 -2.166 .0303 32.487521

Z3 .1821006800E-01 .51704684E-02 3.522 .0004 8.1776955

Z5 -.5582910069E-01 .15568275E-01 -3.586 .0003 3.1164725

Z7 .1140411992E-01 .99845393E-02 1.142 .2534 4.1946755

Z8 -.8298761795E-01 .15933104E-01 -5.209 .0000 3.9317804
+------+

| Limited Dependent Variable Model - TRUNCATE |

| Log likelihood function -392.7103 |

| Threshold values for the model: |

| Lower= .0000 Upper=+infinity |

| Observations after truncation 150 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 8.323045133 3.9597250 2.102 .0356

Z2 -.8414425459E-01 .11941653 -.705 .4810 33.410000

Z3 .5597703506 .21897633 2.556 .0106 9.5319467

Z5 -1.502400347 .61728675 -2.434 .0149 2.8533333

Z7 .1891403416 .37677181 .502 .6157 4.3133333

Z8 -1.349377201 .56454613 -2.390 .0168 3.4466667

Sigma 5.529829399 .65959601 8.384 .0000

+------+

| Partial derivatives of expected val. with |

| respect to the vector of characteristics. |

| They are computed at the means of the Xs. |

| Observations used for means are All Obs. |

| Conditional Mean at Sample Point 5.5614 |

| Scale Factor for Marginal Effects .4843 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 4.030447257 1.9175029 2.102 .0356

Z2 -.4074698319E-01 .57827634E-01 -.705 .4810 33.410000

Z3 .2710696431 .10603962 2.556 .0106 9.5319467

Z5 -.7275396519 .29892205 -2.434 .0149 2.8533333

Z7 .9159149792E-01 .18245232 .502 .6157 4.3133333

Z8 -.6534379609 .27338232 -2.390 .0168 3.4466667

CRAGG = .11140859667898440D+02

? Moment based tests for normality

Tobit ; Lhs = y ; Rhs = XR ; Par$

Matrix ; Beta=b(1:6)$

Create ; bx=beta'xr ; eps=y-bx ; lambda=n01(bx/s)/phi(-bx/s)

; bi= .5*q*(((eps/s)^2-1)/s^2)+.5*(1-q)*bx*lambda/s^3

; ei=(q*eps-(1-q)*s*lambda)/s^2

; a1=ei ;a2=ei*z2 ;a3=ei*z3 ;a4=ei*z5 ;a5=ei*z7

; a6=ei*z8 ;a7=bi ;a8=ei^3 ;a9=ei^4-3*ei^2 $

Namelist ; A=a1,a2,a3,a4,a5,a6,a7,a8,a9$

Matrix ; List ; Chesher=1'a*<a'a>*a'1$

Create ; m1=-(1-q)*(s^3*lambda*(bx/s+2)^2) + q*eps^3

; m2= (1-q)*(s^4*lambda*bx/s*((bx/s)^2+3))

+ q *(eps^4 - 3*s^4)$

Namelist ; G=a1,a2,a3,a4,a5,a6,a7 ; M=m1,m2$

Matrix ; Pagan=m'm-m'g*<g'g>*g'm

; List ; Pagan=1'm*<pagan>*m'1$

CHESHER +------

1| .5622181D+03

PAGAN +------

1| .2031353D+02

? Doubly censored (at 0 and 4) tobit model. Compared to standard case

Tobit ; Lhs = y ; Rhs = XR ; Mar $

Tobit ; Lhs = y ; Rhs = XR ; Mar ; Limits=0,4 $

+------+

| Threshold values for the model: |

| Lower= .0000 Upper=+infinity |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 8.174197436 2.7414456 2.982 .0029

Z2 -.1793325837 .79093240E-01 -2.267 .0234 32.487521

Z3 .5541418128 .13451794 4.119 .0000 8.1776955

Z5 -1.686220493 .40375155 -4.176 .0000 3.1164725

Z7 .3260532488 .25442475 1.282 .2000 4.1946755

Z8 -2.284972720 .40782792 -5.603 .0000 3.9317804

Sigma 8.247080326 .55336401 14.904 .0000

+------+

| Threshold values for the model: |

| Lower= .0000 Upper= 4.0000 |

+------+

Constant 7.900980451 2.8038548 2.818 .0048

Z2 -.1775982087 .79906293E-01 -2.223 .0262 32.487521

Z3 .5323021100 .14116841 3.771 .0002 8.1776955

Z5 -1.616335655 .42439672 -3.809 .0001 3.1164725

Z7 .3241864581 .25387778 1.277 .2016 4.1946755

Z8 -2.207007447 .44983190 -4.906 .0000 3.9317804

Sigma 7.943219445 .87690019 9.058 .0000

+------+

| Partial derivatives of expected val. with |

| respect to the vector of characteristics. |

| Conditional Mean at Sample Point 1.1263 |

| Scale Factor for Marginal Effects .2338 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 1.910805170 .65758415 2.906 .0037

Z2 -.4192088958E-01 .18444435E-01 -2.273 .0230 32.487521

Z3 .1295365141 .31167559E-01 4.156 .0000 8.1776955

Z5 -.3941718881 .93379144E-01 -4.221 .0000 3.1164725

Z7 .7621839800E-01 .59471640E-01 1.282 .2000 4.1946755

Z8 -.5341365586 .94896126E-01 -5.629 .0000 3.9317804

+------+

| Lower= .0000 Upper= 4.0000 |

| Conditional Mean at Sample Point .2257 |

| Scale Factor for Marginal Effects .1229 |

+------+

Constant .9712865849 .34346628 2.828 .0047

Z2 -.2183257619E-01 .95804001E-02 -2.279 .0227 32.487521

Z3 .6543718236E-01 .16101450E-01 4.064 .0000 8.1776955

Z5 -.1987000409 .48288948E-01 -4.115 .0000 3.1164725

Z7 .3985302327E-01 .31004563E-01 1.285 .1987 4.1946755

Z8 -.2713127490 .48803373E-01 -5.559 .0000 3.9317804

? Poisson and Negative Binomial Regressions. Uncensored

Poisson ; Lhs=y ; rhs = Xr ; MarginalEffects $

Negbin ; Lhs=y ; rhs = Xr ; MarginalEffects $

? Censored Poisson and Negative Binomial Models, censored at 4

Create ; yc=y ; If(yc>=4)yc=4 $

Poisson ; Lhs=yc ; Rhs = Xr ; Limit=4 ; MarginalEffects$

? Create predictions from least restrictive model. Convert

? conditional means to integers, then censor.

Negbin ; Lhs=yc ; Rhs = Xr ; Limit=4 ; Margin ; keep=yfnb$

Create ; Iyfnb=int(yfnb) ; If(iyfnb>4)iyfnb=4$

+------+

| Poisson Regression |

| Log likelihood function -1427.037 |

| Restricted log likelihood -1709.723 |

| Chi- squared = 4125.90994 RsqP= .0800 |

| G - squared = 2360.08448 RsqD= .1933 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 2.533905282 .19692367 12.867 .0000

Z2 -.3225529750E-01 .58514053E-02 -5.512 .0000 32.487521

Z3 .1156984318 .99084864E-02 11.677 .0000 8.1776955

Z5 -.3540371394 .30892099E-01 -11.460 .0000 3.1164725

Z7 .7982824190E-01 .19448856E-01 4.105 .0000 4.1946755

Z8 -.4094427239 .27381245E-01 -14.953 .0000 3.9317804

+------+

| Partial derivatives of expected val. with |

| respect to the vector of characteristics. |

| Conditional Mean at Sample Point 1.4559 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 3.689129986 .39117889 9.431 .0000

Z2 -.4696070767E-01 .11623520E-01 -4.040 .0001 32.487521

Z3 .1684461361 .19682706E-01 8.558 .0000 8.1776955

Z5 -.5154450866 .61365588E-01 -8.400 .0000 3.1164725

Z7 .1162224820 .38634166E-01 3.008 .0026 4.1946755

Z8 -.5961104549 .54391454E-01 -10.960 .0000 3.9317804

+------+

| Log likelihood function -728.2441 |

| Restricted log likelihood -1427.037 |

| Chi-squared 1397.586 |

| Degrees of freedom 1 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 2.189665176 .85899305 2.549 .0108

Z2 -.2623881896E-02 .17955428E-01 -.146 .8838 32.487521

Z3 .8481865225E-01 .40012554E-01 2.120 .0340 8.1776955

Z5 -.4222270934 .17050728 -2.476 .0133 3.1164725

Z7 .6044301285E-01 .90859681E-01 .665 .5059 4.1946755

Z8 -.4313313504 .16739868 -2.577 .0100 3.9317804

Overdispersion parameter for negative binomial model

Alpha 7.014805680 .94459163 7.426 .0000

+------+

| Partial derivatives of expected val. with |

| respect to the vector of characteristics. |

| Conditional Mean at Sample Point 1.4984 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 3.280911000 1.8007047 1.822 .0685

Z2 -.3931524815E-02 .37639913E-01 -.104 .9168 32.487521

Z3 .1270890418 .83878204E-01 1.515 .1297 8.1776955

Z5 -.6326490143 .35743393 -1.770 .0767 3.1164725

Z7 .9056551106E-01 .19046889 .475 .6344 4.1946755

Z8 -.6462904866 .35091738 -1.842 .0655 3.9317804

+------+

| Poisson Regression |

| Log likelihood function -747.7541 |

| RIGHT Censored Data: Threshold = 4. |

| Chi- squared = 1520.43723 RsqP= .0799 |

| G - squared = 1077.99336 RsqD= .1877 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 1.899932460 .28256837 6.724 .0000

Z2 -.3284957645E-01 .83771861E-02 -3.921 .0001 32.487521

Z3 .1053474148 .14041819E-01 7.502 .0000 8.1776955

Z5 -.3233479425 .43740859E-01 -7.392 .0000 3.1164725

Z7 .7984038573E-01 .27533200E-01 2.900 .0037 4.1946755

Z8 -.3896778919 .39122373E-01 -9.960 .0000 3.9317804

+------+

| Partial derivatives of expected val. with |

| respect to the vector of characteristics. |

| Conditional Mean at Sample Point .7663 |

| Scale Factor for Marginal Effects .7166 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 1.361437133 .28978016 4.698 .0000

Z2 -.2353906474E-01 .75918324E-02 -3.101 .0019 32.487521

Z3 .7548893733E-01 .14750440E-01 5.118 .0000 8.1776955

Z5 -.2317018658 .45888605E-01 -5.049 .0000 3.1164725

Z7 .5721133153E-01 .24384424E-01 2.346 .0190 4.1946755

Z8 -.2792320060 .45043450E-01 -6.199 .0000 3.9317804

+------+

| Negative Binomial Regression |

| Log likelihood function -482.0505 |

| Restricted log likelihood -747.7541 |

| Chi-squared 531.4072 |

| Degrees of freedom 1 |

| RIGHT Censored Data: Threshold = 4. |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 4.792788283 1.1636038 4.119 .0000

Z2 -.1659616715E-01 .24963901E-01 -.665 .5062 32.487521

Z3 .1744625408 .56779368E-01 3.073 .0021 8.1776955

Z5 -.7229290289 .19807844 -3.650 .0003 3.1164725

Z7 .8998362814E-01 .11558144 .779 .4363 4.1946755

Z8 -.8544311272 .21634356 -3.949 .0001 3.9317804

Overdispersion parameter for negative binomial model

Alpha 9.395956878 1.3533645 6.943 .0000

+------+

| Partial derivatives of expected val. with |

| respect to the vector of characteristics. |

| Conditional Mean at Sample Point .7170 |

| Scale Factor for Marginal Effects .2577 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 1.235198281 .79158359 1.560 .1187

Z2 -.4277167262E-02 .71500734E-02 -.598 .5497 32.487521

Z3 .4496251822E-01 .30220047E-01 1.488 .1368 8.1776955

Z5 -.1863134028 .11685569 -1.594 .1108 3.1164725

Z7 .2319059725E-01 .33257461E-01 .697 .4856 4.1946755

Z8 -.2202041478 .13847023 -1.590 .1118 3.9317804

Histogram; Rhs=yc$ (Actual data)

Histogram; Rhs=iyfnb$(Predictions)

Histogram for YC NOBS= 601, Too low: 0, Too high: 0

Bin Lower limit Upper limit Frequency Cumulative Frequency

======

0 .000 1.000 451 ( .7504) 451( .7504)

1 1.000 2.000 34 ( .0566) 485( .8070)

2 2.000 3.000 17 ( .0283) 502( .8353)

3 3.000 4.000 19 ( .0316) 521( .8669)

4 4.000 5.000 80 ( .1331) 601(1.0000)

Histogram for IYFNB NOBS= 601, Too low: 0, Too high: 0

Bin Lower limit Upper limit Frequency Cumulative Frequency

======

0 .000 1.000 251 ( .4176) 251( .4176)

1 1.000 2.000 96 ( .1597) 347( .5774)

2 2.000 3.000 50 ( .0832) 397( .6606)

3 3.000 4.000 34 ( .0566) 431( .7171)

4 4.000 5.000 170 ( .2829) 601(1.0000)

? Zero inflated (split population) Poisson model+ Tobit(0,4)

Poisson ; Lhs=yc ; Rhs = XR

; ZIP; Rh2=Xr;par; keep=yfpz ; Mar $

Matrix ; Beta = B(1:6) ; Gamma = B(7:12)$

Create ; Lambda=exp(Beta'xr);qi=lgp(gamma'xr)

; Ey=(1-qi)*lambda ; Iey=int(ey)$

Histogram; Rhs=Iey$

Tobit ; Lhs=yc ; Rhs = XR ; Alg=BFGS ;Mar $

Tobit ; Lhs=yc ; Rhs = XR ; Limits = 0,4 ; Alg=BFGS ;Mar $

Histogram for IEY NOBS= 601, Too low: 0, Too high: 0

Bin Lower limit Upper limit Frequency Cumulative Frequency

======

0 .000 1.000 448 ( .7454) 448( .7454)

1 1.000 2.000 134 ( .2230) 582( .9684)

2 2.000 3.000 17 ( .0283) 599( .9967)

3 3.000 4.000 2 ( .0033) 601(1.0000)

+------+

| Zero Altered Poisson Regression Model |

| Logistic distribution used for splitting model. |

| ZAP term in probability is F[tau x Z(i) ] |

| Comparison of estimated models |

| Pr[0|means] Number of zeros Log-likelihood |

| Poisson .55783 Act.= 451 Prd.= 335.3 -771.44432 |

| Z.I.Poisson .77364 Act.= 451 Prd.= 465.0 -551.72760 |

| Note, the ZIP log-likelihood is not directly comparable. |

| ZIP model with nonzero Q does not encompass the others. |

| Vuong statistic for testing ZIP vs. unaltered model is 21.6436 |

| Distributed as standard normal. A value greater than |

| +1.96 favors the zero altered Z.I.Poisson model. |

| A value less than -1.96 rejects the ZIP model. |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Poisson/Negbin regression model

Constant 1.274187369 .43940971 2.900 .0037

Z2 -.4219823370E-02 .12229828E-01 -.345 .7301 32.487521

Z3 .3312258287E-01 .23127736E-01 1.432 .1521 8.1776955

Z5 -.9085096098E-01 .72054203E-01 -1.261 .2074 3.1164725

Z7 .2052418829E-01 .44126404E-01 .465 .6418 4.1946755

Z8 -.8166127920E-01 .66574722E-01 -1.227 .2200 3.9317804

Zero inflation model

Constant -1.848860263 .66436621 -2.783 .0054

Z2 .3970949740E-01 .19046738E-01 2.085 .0371 32.487521

Z3 -.9814600629E-01 .31795289E-01 -3.087 .0020 8.1776955

Z5 .3062225236 .95089852E-01 3.220 .0013 3.1164725

Z7 -.6770594854E-01 .60739793E-01 -1.115 .2650 4.1946755

Z8 .4577650236 .94870568E-01 4.825 .0000 3.9317804

ZIP

+------+

| Partial derivatives of expected val. with |

| respect to the vector of characteristics. |

| They are computed at the means of the Xs. |

| Observations used for means are All Obs. |

| Conditional Mean at Sample Point .0063 |

| Scale Factor for Marginal Effects -.3438 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 2.899747536 .57896387 5.009 .0000

Z2 -.2523628400E-01 .12985077E-01 -1.943 .0520 32.487521

Z3 .9869128559E-01 .26718883E-01 3.694 .0002 8.1776955

Z5 -.2879288809 .85416029E-01 -3.371 .0007 3.1164725

Z7 .6436057742E-01 .46300314E-01 1.390 .1645 4.1946755

Z8 -.3437579550 .79602625E-01 -4.318 .0000 3.9317804

Tobit(0)

+------+

| Partial derivatives of expected val. with |

| respect to the vector of characteristics. |

| They are computed at the means of the Xs. |

| Observations used for means are All Obs. |

| Conditional Mean at Sample Point 1.1263 |

| Scale Factor for Marginal Effects .2338 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant 1.910805168 .65758415 2.906 .0037

Z2 -.4192088954E-01 .18444435E-01 -2.273 .0230 32.487521

Z3 .1295365140 .31167559E-01 4.156 .0000 8.1776955

Z5 -.3941718875 .93379144E-01 -4.221 .0000 3.1164725

Z7 .7621839725E-01 .59471639E-01 1.282 .2000 4.1946755

Z8 -.5341365577 .94896126E-01 -5.629 .0000 3.9317804

Tobit(0,4)

+------+

| Partial derivatives of expected val. with |

| respect to the vector of characteristics. |

| They are computed at the means of the Xs. |

| Observations used for means are All Obs. |

| Conditional Mean at Sample Point .2257 |

| Scale Factor for Marginal Effects .1229 |

+------+

+------+------+------+------+------+------+

+------+------+------+------+------+------+

Constant .9712865866 .34346628 2.828 .0047

Z2 -.2183257607E-01 .95804001E-02 -2.279 .0227 32.487521

Z3 .6543718214E-01 .16101450E-01 4.064 .0000 8.1776955

Z5 -.1987000414 .48288948E-01 -4.115 .0000 3.1164725

Z7 .3985302304E-01 .31004563E-01 1.285 .1987 4.1946755

Z8 -.2713127494 .48803373E-01 -5.559 .0000 3.9317804